Abstract
The two-dimensional bin packing problem (2BP) consists in packing a set of rectangular items into rectangular, equally-sized bins. The problem is NP-hard and has a multitude of real world applications. We consider the case where the items are oriented and guillotine cutting is free. In this paper we first present a review of well-know heuristics for the 2BP and then propose a new ILP model for the problem. Moreover, we develop a multi-start algorithm based on a probabilistic version of the LGFi heuristic from the literature. Results are compared to other well-known heuristics, using data sets provided in the literature. The obtained experimental results show that the proposed algorithm returns excellent solutions. With an average percentage deviation of 1.8% from the best know lower bounds it outperformes the other algorithms by 1.1% − 5.7%. Also for 3 of the 500 instances we tested a new upper bound was found.
This work was supported by the binational grant Acciones Integradas ES16-2009 (Austria) and MEC HA2008-0005 (Spain), and by grant TIN2007-66523 (FORMALISM) of the Spanish government. In addition, Christian Blum acknowledges support from the Ramón y Cajal program of the Spanish Government of which he is a research fellow.
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Baumgartner, L., Schmid, V., Blum, C. (2011). Solving the Two-Dimensional Bin Packing Problem with a Probabilistic Multi-start Heuristic. In: Coello, C.A.C. (eds) Learning and Intelligent Optimization. LION 2011. Lecture Notes in Computer Science, vol 6683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25566-3_6
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DOI: https://doi.org/10.1007/978-3-642-25566-3_6
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